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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Thu Nov 10, 2011 12:52 pm

How many positive integers less than 10,000 are there in which the sum of digits equals 5?

A)31
B)51
C)56
D)62
E)93

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Source: Beat The GMAT — Problem Solving | Thu Nov 10, 2011 12:52 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Nov 10, 2011 1:09 pm

MBA.Aspirant wrote:How many positive integers less than 10,000 are there in which the sum of digits equals 5?

A)31
B)51
C)56
D)62
E)93

I posted a solution here:

https://www.beatthegmat.com/experts-any- ... 82307.html

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Nov 10, 2011 1:10 pm

No of one digit numbers whose digits sum to 5 = 1 (Just the number 5)

No of two digit numbers whose digits sum to 5 = 5 (23,32,41,14,50)

No of three digit numbers whose digits sum to 5 = 15 (500,401,104,410,140,302,203,320,230,311,113,131,221,212,122

No of four digit numbers whose digits sum to 5 = 35
The possible sets are
(1,2,2,0) - 9 different numbers
(1,1,1,2) - 4 different numbers
(1,3,1,0) - 9 different numbers
(3,2,0,0) - 6 different numbers
(4,1,0,0) - 6 different numbers
(5,0,0,0) - 1 number

Total number of positive integers less than 10000 with the sum of digits equal to 5 = 35+15+5+1 = 56

IMO C

Anil Gandham
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